Second-Order Linear Non-Homogeneous Equation with constant coefficient

[simplemind]

Msaada:will someone kindly solve this(I am bit mathematically rusty off late)
Ay"+By'+Cy=D+E(sinwt)

 

[Kijakazi]

Msaada:will someone kindly solve this(I am bit mathematically rusty off late)
Ay"+By'+Cy=D+E(sinwt)

Anza kukotoa ulipokwama nitaendelea kama nia yako hasa ni kujifunza!

Isitoshe lazima mfundishaji ajue pa kuanzia!

 

[simplemind]

Anza kukotoa ulipokwama nitaendelea kama nia yako hasa ni kujifunza! Isitoshe lazima mfundishaji ajue pa kuanzia!

Neighbours kid ameomba msaada tatizo hii kitu nimepitia way back in history, hivo na hitaji jibu redi medi or may be step by step guide.

 

[Kijakazi]

Neighbours kid ameomba msaada tatizo hii kitu nimepitia way back in history, hivo na hitaji jibu redi medi or may be step by step guide.

Basi hapo pagumu kwangu kwani huwa sipendi kumtafunia Mtu kila kitu, kama Mtu anapenda kujifunza ni lazima twende ngazi kwa ngazi ili tukifika mwisho basi na yeye awe ameelewa, kwani haina maana yoyoyte mimi kuandika jibu kama utakuwa haujaelewa!

 

[Mjomba Fujo]

Wabongo bwana, mtu anaomba msaada unaanza kujisifu sifu mimi mimi, kama unajua toa msaada.

Majibu kama haya huwezi kuyakuta yahoo answers, watu wapo straight mtu ana swali anajibiwa ila huku kwetu hata kama unajua jibu mtu utajivutaa, kama huna msaada kwa wengine bora ukae kimya.

 

[Mwanamayu]

Msaada:will someone kindly solve this(I am bit mathematically rusty off late)
Ay"+By'+Cy=D+E(sinwt)

Jaribu kwenye YouTube pia.

 

[simplemind]

mdau wangu hapo utasolve nini kama hamna namba..

Wadua wa advanced mathematics wanafahamu mtiririko.

 

[Darius]

mdau wangu hapo utasolve nini kama hamna namba..

hahaha...ww n mdau wa pure math or not

 

[meningitis]

The best mathematician was homosexual!
#AlanTuring

 

[simplemind]

The best mathematician was homosexual!
#AlanTuring

Shida yangu jawabu hayo mengine ni ya Alan Turing na recording angel.

 

[Charles Mandela]

Darius na simplemind ishu iko hivi:

Ay" + By' + Cy = D + E(sinwt).

This is a form of equation where A, B, C, D, E and w are constants and t is a parameter.

Now separate the equation:
Ay" + By' + Cy = D........Equation i

Ay" + By' + Cy = E(sinwt).........Equation ii

Then;

For Equation i
Ay" + By' + Cy = D is in form of f(X) = M ,where M is a constant and f(X) = y. Thus y = M

So if y = M; Then y' = 0 and y" = 0. Since we differentiating constant number, all derivatives become zero ( 0 ).

Then substitute the values above in Equation i

From: Ay'' + By' + Cy = D where y = M; y' = 0 and y" = 0

Then: A(0) + B(0) + C(M) = D

Then: C(M) = D , thus the value of M = D/C but M = f(x) = y

Thus the value of y = D/C


For Equation ii


Ay'' + By' + Cy = E(sinwt) is in form of f(X) = M(sinwt) + N(coswt) and f(X) = y.

Thus y = M(sinwt) + N(coswt)

So if, y = M(sinwt) + N(coswt)

Then y' =Mw(coswt) - Nw(sinwt)

Then y'' = -Mw(sinwt) - Nw(coswt)

Substitute the values above into Equation ii

A(-Mw(sinwt) - Nw(coswt)) + B(Mw(coswt) - Nw(sinwt)) + C(M(sinwt) + N(coswt)) = E(sinwt)
-AMw(sinwt) - ANw(coswt) + BMw(coswt) - BNw(sinwt) + CM(sinwt) + CN(coswt) = E(sinwt) + 0(coswt)

By comparing the values of Sine and Cosine:

For Sine

-AMw(sinwt) - BNw(sinwt) + CM(sinwt) = E(sinwt)...... Equation iii

We flash out (sinwt) and the equation will be: -AMw - BNw + CM = E

Then: M(C - Aw) - NBw = E ;

But (C - Aw) and Bw are both constants.

Then let (C - Aw) be m and Bw be m. Since all values are both constant.

Thus Mm - Nm = E....... Equation iv


For Cosine

- ANw(coswt) + BMw(coswt) + CN(coswt) = 0(coswt)...... Equation v

We flash out (coswt) and the equation will be:

-ANw + BMw + CN = 0

N(C - Aw) + BMw = 0

But (C - Aw) & Bw are both constants.

Then Let (C - Aw) be n and Bw be n.

Thus: Nn + Mn = 0 ..... Equation vi

Thus by combining Equation iv & Equation vi we get;
Mm - Nm = E....... Equation iv
Nn + Mn = 0 ........ Equation vi

Now, let us solve simultaneous equation to obtain the values of M & N where m and n are both constants.

In Equation vi : Nn = -Mn

Thus N = -M, Since n and n are constants. And any valuable multiplied by constant, the answer will be constant.

So let constant M(n) be k .

Therefore the value of N will be - k.

Substitute the value of N = -k into Equation iv
Mm - Nm = E;

We get Mm + km = E
Then Mm = E - km
Then M = (E - km)/m

So let constant (E - km)/m be k .

Therefore the value of M will be k.

Thus the value of y = k(sinwt) - k(coswt)

Since the value of y = y1 + y2. The overall value of y will be given as

y = D/C + k2(sinwt) - k1(coswt) where C, D, k1 and k2 are both cosntants

 

[mng'ato]

Maziku Masunga Jr.,

Mambo ya old moshi haya au iliboru, hahah

 

[Kiteitei]

Maziku Masunga Jr.,

Macho yamenitoka kama fundi saa!!!hakyaNaNi sielewi kitu hapo!!!!!

 

[Kiteitei]

Maziku Masunga Jr.,

Macho yamenitoka kama fundi saa!!!hakyaNaNi sielewi kitu hapo!!!

 

[Kingmairo]

Maziku Masunga Jr.,

Wale wa soshologi na viingereza vyenu kujeni huku.

Ha ha ha

 

[Ngalikihinja]

Wale wa soshologi na viingereza vyenu kujeni huku. Ha ha ha

Kwa kifupi MANGWINI

 

[CHAMVIGA]

mdau wangu hapo utasolve nini kama hamna namba..

Mambo ya differential equation hayo sio lazima number. 2nd order linear non hormogeneous equation ndio ijulikanavyo.

 

[simplemind]

Maziku Masunga Jr.,

Ahsante. Nothing to add apart from solution to complementary equation Ay"+By'+Cy=0 ( a trivial matter of solving a quadratic equation)

 

[Darius]

Mambo ya NDANDA BOYS HIGH SCHOOL HAYO EGM oneeeee..................now daaah nimeshazeeka



Maziku Masunga Jr.,

 

[rolla]

macho yamenitoka kama fundi saa!!!hakyaNaNi sielewi kitu hapo!!!!!

Umenifurahisha.... Nimecheka hadi nimeamsha mtoto.